The researches on the efficiency of edge attack strategies for complex networks often ignored the edge's attack cost in the past.Aiming at this problem

we propose a new method to investigate the network robustness based on edge's attack cost in this paper.This method takes the factor of edge's attack cost into account.Edge's weight is used to approximately measure the attack cost of edges.The relative size of giant connected component is used to quantify the network robustness.The robustness of synthetic datasets and real networks is investigated when the attack cost of edges is present.Moreover

the impacts of edge's weight on network robustness are discussed.The experimental results show that when the edge's attack cost is low

the attack effect of low-weight removal strategy (LW) is the best for complex networks.For synthetic datasets

BA(Barabasi-Albert) networks are more robust than WS(Watts-Strogatz) networks under high-weight removal strategy (HW).The robustness of real networks can be optimized by adjusting the edge's weights.Compared with existing methods

our method may be more practical for investigating the network robustness.Simulation results show the validity and feasibility of the method.